Joseph Migler Introduction to K-theory and K-homology
Oct. 07, 2014 12:10pm (MATH …
Kempner
Claire Levaillant (UC Santa Barbara)
X
Classical computers function with bits that are 0 and 1. Instead quantum computers function with states that are complex linear combinations of quantum bits |0> and |1>. In this talk we will give an overview of how to make quantum gates, that is how to mathematically and physically realize the unitary transformations that make a state evolve to another state.
Our approach is based on the pioneering work of Michael Freedman, Chetan Nayak and Sankar Das Sarma among others in topological quantum computation. An important physical operation consists of braiding quasi-particles which are named anyons.
Making a braid on anyons consists of interchanging their positions. The mathematical theory which we use behind the physics of braiding anyons is the Kauffman-Jones version of
SU(2) Chern-Simons theory at level 4. We will introduce this theory and show how to make some of the quantum gates that make quantum computation universal, that is, it is possible with these very few gates to obtain good approximations to any desired gate.
The speaker will discuss the tangent groupoid, an important groupoid that appears in geometry and analysis.
The tangent groupoid Sponsored by the Meyer Fund
Oct. 07, 2014 2pm (MATH 350)
Lie Theory
Cliff Blakestad (CU)
X
The Weil Conjectures (now theorems) suggest deep connections between counting solutions to equations over finite fields and the topology of the complex solutions to those same equations. We will explore how one can use these connections to apply topological information about complex spaces toward answering counting questions related to finite fields and see some of the challenges involved in this approach.